If only logic was the driving force of the vote on the Brexit deal, we could guess the result on Tuesday

The interlocking preferences, wishful thinking and tribal loyalties of 650 MPs make the vote, and what follows, impossible to predict

May's deal will likely be defeated. A lot depends on how she responds to the vote (EPA)

If you asked a professor of logic for the way out of the Brexit tangle, she would say it is perfectly simple. Theresa May’s deal comes closest to what the greatest number of MPs say they want, so they ought to go for that.

Yet the prime minister’s deal is heading for defeat on Tuesday, probably by a huge margin. It is not a logician we need but a games theorist, a behavioural psychologist and a dramatist, all of them on hallucinogens, to make sense of this lot.

We are dealing with interlocking preferences, wishful thinking and tribal loyalties that make the vote, and what follows, impossible to predict.

Amber Rudd, a cabinet minister, unusually spelt out her preferences in an interview with The Times this morning. First she would rather have May’s deal; if she can’t have that she would opt for staying in the EU single market and customs union (often called the Norway option, which is misleading because Norway isn’t in the customs union); and if she can’t have that she would want a referendum in which she would vote to remain in the EU.

Each MP has their own order of preference, usually including several options that are less realistic than Rudd’s. At the moment, May’s deal is probably the least popular of all the options. But it is up against options that do not exist, such as the idea of renegotiating a “better” deal.

The professor of logic would simplify the options to the three possible end states: leaving with a deal, leaving without a deal and staying in the EU. If we are leaving with a deal, that deal would include a guarantee of an open border in Ireland, known as the backstop. This is the heart of May’s problem.

Every time you see or hear the word “backstop”, swap it for “guarantee of an open Irish border” and see how it sounds. Even Jeremy Corbyn says he is against it. “There certainly wouldn’t be a ‘backstop’ from which you can’t escape,” he said on Friday, referring to the terms of the withdrawal agreement that give the EU the power to require the UK to keep the Irish border open.

In principle, it is odd to bind a sovereign nation into an international agreement with no escape clause, but in practice it is not something a UK government would want to get out of anyway. Does Corbyn think that at some stage a Labour government would want to impose checks and controls on goods crossing the Irish border?

Labour’s position makes no sense, and is likely to be exposed in the next few weeks, but the immediate crisis is in the Conservative Party. Many of its MPs really would rather have a hard border in Ireland, although they usually pretend it could be managed by technology that does not yet exist.

So May’s deal will be defeated on Tuesday, either by a large margin or, if the amendment in the name of Hilary Benn, the Labour chair of the Brexit select committee, is passed, by a smaller one. The Benn amendment is opposed both to May’s deal and to a no-deal Brexit, which means the Tory hard Brexiteers won’t vote for it.

I don’t think the prime minister will try to postpone the vote. It is not clear that she can, but I don’t think she would want to. This is a defeat she has to suffer before she can move on to try to win an eventual victory.

A lot depends on how she responds to the vote. It may be that the group psychology of Tory MPs becomes unstable and enough of them decide for different reasons that they need a new leader, although we seem at the moment a long way from the target number of 158 (half the parliamentary party).

She could say she will go to Brussels for Thursday’s summit and demand changes to avoid a no-deal Brexit. The trouble is that the EU knows that most MPs don’t want to leave without a deal. In any case, the backstop – by which I mean the guarantee of an open border in Ireland – is not negotiable. May tried for 10 months to shift the EU side on that and got nowhere.

She might announce that, although she doesn’t want one, she’ll ask the Commons if it wants to put her deal to a referendum. This would put the Labour Party on the spot. Corbyn doesn’t want a referendum, but there is probably a majority in his shadow cabinet for it.

Even if Labour came out for it, though, a proposal for a referendum is likely to be defeated, which would allow May to say parliament had to decide between her deal and a no-deal Brexit. On the other hand, maybe parliament would vote for a referendum, in which case she would have to ask the EU27 to postpone Brexit so that we could hold one.

I don’t know what is going to happen, and I am sceptical about anyone who claims to know.